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  • @article{RISC4408,
    author = {Stavros Garoufalidis and Christoph Koutschan},
    title = {{The non-commutative A-polynomial of (-2,3,n) pretzel knots}},
    language = {english},
    abstract = {We study q-holonomic sequences that arise as the colored Jones polynomial of knots in 3-space. The minimal-order recurrence for such a sequence is called the (non-commutative) A-polynomial of a knot. Using the method of guessing, we obtain this polynomial explicitly for the K_p=(-2,3,3+2p) pretzel knots for p=-5, ..., 5. This is a particularly interesting family since the pairs (K_p, -K_{-p}) are geometrically similar (in particular, scissors congruent) with similar character varieties. Our computation of the non-commutative A-polynomial (a) complements the computation of the A-polynomial of the pretzel knots done by the first author and Mattman, (b) supports the AJ Conjecture for knots with reducible A-polynomial and (c) numerically computes the Kashaev invariant of pretzel knots in linear time. In a later publication, we will use the numerical computation of the Kashaev invariant to numerically verify the Volume Conjecture for the above mentioned pretzel knots.},
    journal = {Experimental Mathematics},
    volume = {21},
    number = {3},
    pages = {241--251},
    isbn_issn = {ISSN 1058-6458},
    year = {2012},
    refereed = {yes},
    length = {11},
    url = {http://www.risc.jku.at/people/ckoutsch/pretzel/}
    }